Part VI
Verification
E. Algorithm and software checks · Closed gap stays closed, single step
A gap with a clearance of 0.25 mm is closed at the second iteration. The trial displacement is exactly 0.25 mm, and the stop pushes back with a trial reaction of −2.0 N against further positive movement. Should the gap stay closed? This case tests one classification step on its own, with no frame solve around it.
1.Inputs.
Illustrative values, taken from no standard and chosen so the arithmetic can be followed by hand. Most do not describe a real pipe; read them in any consistent set of units.
| Quantity | Symbol | Value |
|---|---|---|
| Iteration | — | 2 |
| Maximum iterations | — | 6 |
| Active-set residual tolerance | — | 0.0 (count) |
| Gap clearance | c | 0.25 mm |
| Trial displacement | u | 0.25 mm |
| Trial reaction | R | −2.0 N |
| Prior state | — | active (closed) |
2.Method.
A closed gap is judged by the sign of its contact force, not by its displacement, which sits at the clearance. A gap that closes on positive movement bears with a negative reaction. The −2.0 N reaction has that sign, so contact persists and the gap stays closed. No support changes state, so the active-set residual is zero and the step is converged.
3.Results.
| Quantity | Expected |
|---|---|
| Clearance | 0.25 mm |
| Trial displacement | 0.25 mm |
| Trial reaction | −2.0 N |
| State after the step | active (closed) |
| Active-set residual | 0.0 |
The tests check that:
- The gap stays active (closed), and no support is reported as changed.
- The active-set residual is exactly 0.0 and the step is reported as converged with no diagnostic.
- Every input and expected value carries an explicit unit, and the case’s source note exists. This is a bookkeeping check, not a mechanics check.
What it shows. Checks the supports’ final states, the iteration count and the balance of forces. Movements and reactions are not compared with a hand calculation.
Path exercised. The benchmark calls the solver’s components directly: elements, loads, frame solver and stress recovery. It does not go through the program’s own model-to-solve path.
Agreement. No numerical tolerance band applies. The tests require the exact expected support state, changed-support count and convergence flag; nothing is compared within a margin. Long values are shown here to seven significant figures; the tests compare the full values in the record.
4.Run it yourself.
cd projects/chirality-piping cargo test --manifest-path validation/benchmarks/nonlinear/Cargo.toml fixtures_are_public_original_and_unit_aware cargo test --manifest-path validation/benchmarks/nonlinear/Cargo.toml active_set_gap_lift_off_and_friction_outcomes_are_deterministic
Hand calculation:
validation/hand_calcs/nonlinear/gap_closure.md.
Test record, with the recorded run of 2026-07-10:
nl-gap-closure-original.md.